6,034 research outputs found
Rigid motions: action-angles, relative cohomology and polynomials with roots on the unit circle
Revisiting canonical integration of the classical solid near a uniform
rotation, canonical action angle coordinates, hyperbolic and elliptic, are
constructed in terms of various power series with coefficients which are
polynomials in a variable depending on the inertia moments. Normal forms
are derived via the analysis of a relative cohomology problem and shown to be
obtainable without the use of ellitptic integrals (unlike the derivation of the
action-angles). Results and conjectures also emerge about the properties of the
above polynomials and the location of their roots. In particular a class of
polynomials with all roots on the unit circle arises.Comment: 26 pages, 1 figur
A direct proof of Kim's identities
As a by-product of a finite-size Bethe Ansatz calculation in statistical
mechanics, Doochul Kim has established, by an indirect route, three
mathematical identities rather similar to the conjugate modulus relations
satisfied by the elliptic theta constants. However, they contain factors like
and , instead of . We show here that
there is a fourth relation that naturally completes the set, in much the same
way that there are four relations for the four elliptic theta functions. We
derive all of them directly by proving and using a specialization of
Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics
Street Gangs and Coercive Control: The Gendered Exploitation of Young Women and Girls in County Lines
This paper explores young women and girlsâ participation in gangs and âcounty linesâ drug sales. Qualitative interviews and focus groups with criminal justice and social service professionals found that women and girls in gangs often are judged according to androcentric, stereotypical norms that deny gender-specific risks of exploitation. Gangs capitalise on the relative âinvisibilityâ of young women to advance their economic interests in county lines and stay below police radar. The research shows gangs maintain control over women and girls in both physical and digital spaces via a combination of threatened and actual (sexual) violence and a form of economic abuse known as debt bondage; tactics readily documented in the field of domestic abuse. This paper argues that coercive control offers a new way of understanding and responding to these gendered experiences of gang life, with important implications for policy and practic
The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
An S-matrix satisying the Yang-Baxter equation with symmetries relevant to
the AdS_5xS^5 superstring has recently been determined up to an unknown scalar
factor. Such scalar factors are typically fixed using crossing relations,
however due to the lack of conventional relativistic invariance, in this case
its determination remained an open problem.
In this paper we propose an algebraic way to implement crossing relations for
the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a
Hopf-algebraic formulation of crossing in terms of the antipode and introduce
generalized rapidities living on the universal cover of the parameter space
which is constructed through an auxillary, coupling constant dependent,
elliptic curve. We determine the crossing transformation and write functional
equations for the scalar factor of the S-matrix in the generalized rapidity
plane.Comment: 27 pages, no figures; v2: sign typo fixed in (24), everything else
unchange
Canonical transformations in three-dimensional phase space
Canonical transformation in a three-dimensional phase space endowed with
Nambu bracket is discussed in a general framework. Definition of the canonical
transformations is constructed as based on canonoid transformations. It is
shown that generating functions, transformed Hamilton functions and the
transformation itself for given generating functions can be determined by
solving Pfaffian differential equations corresponding to that quantities. Types
of the generating functions are introduced and all of them is listed.
Infinitesimal canonical transformations are also discussed. Finally, we show
that decomposition of canonical transformations is also possible in
three-dimensional phase space as in the usual two-dimensional one.Comment: 19 pages, 1 table, no figures. Accepted for publication in Int. J.
Mod. Phys.
Vacuum polarization induced by a uniformly accelerated charge
We consider a point charge fixed in the Rindler coordinates which describe a
uniformly accelerated frame. We determine an integral expression of the induced
charge density due to the vacuum polarization at the first order in the fine
structure constant. In the case where the acceleration is weak, we give
explicitly the induced electrostatic potential.Comment: 13 pages, latex, no figures, to appear in Int. J. Theor. Phys
Partition function of the eight-vertex model with domain wall boundary condition
We derive the recursive relations of the partition function for the
eight-vertex model on an square lattice with domain wall boundary
condition. Solving the recursive relations, we obtain the explicit expression
of the domain wall partition function of the model. In the
trigonometric/rational limit, our results recover the corresponding ones for
the six-vertex model.Comment: Latex file, 20 pages; V2, references adde
On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain
A generalization of Jacobi's elliptic functions is introduced as inversions
of hyperelliptic integrals. We discuss the special properties of these
functions, present addition theorems and give a list of indefinite integrals.
As a physical application we show that periodic kink solutions (kink chains) of
the double sine-Gordon model can be described in a canonical form in terms of
generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table
A new Q-matrix in the Eight-Vertex Model
We construct a -matrix for the eight-vertex model at roots of unity for
crossing parameter with odd , a case for which the existing
constructions do not work. The new -matrix \Q depends as usual on the
spectral parameter and also on a free parameter . For \Q has the
standard properties. For , however, it does not commute with the
operator and not with itself for different values of the spectral
parameter. We show that the six-vertex limit of \Q(v,t=iK'/2) exists.Comment: 10 pages section on quasiperiodicity added, typo corrected, published
versio
Coordinate-invariant Path Integral Methods in Conformal Field Theory
We present a coordinate-invariant approach, based on a Pauli-Villars measure,
to the definition of the path integral in two-dimensional conformal field
theory. We discuss some advantages of this approach compared to the operator
formalism and alternative path integral approaches. We show that our path
integral measure is invariant under conformal transformations and field
reparametrizations, in contrast to the measure used in the Fujikawa
calculation, and we show the agreement, despite different origins, of the
conformal anomaly in the two approaches. The natural energy-momentum in the
Pauli-Villars approach is a true coordinate-invariant tensor quantity, and we
discuss its nontrivial relationship to the corresponding non-tensor object
arising in the operator formalism, thus providing a novel explanation within a
path integral context for the anomalous Ward identities of the latter. We
provide a direct calculation of the nontrivial contact terms arising in
expectation values of certain energy-momentum products, and we use these to
perform a simple consistency check confirming the validity of the change of
variables formula for the path integral. Finally, we review the relationship
between the conformal anomaly and the energy-momentum two-point functions in
our formalism.Comment: Corrected minor typos. To appear in International Journal of Modern
Physics
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